Account Of Frictional Forces Research Articles

One-Dimensional Plane Monochromatic Filtration Waves

Equations and relations to describe one-dimensional plane monochromatic fi ltration waves in a homogeneous isotropic porous medium have been obtained. To this end, use was made of the equation of motion of a liquid phase with account of frictional forces, which in the case of steady-state fi ltration with parallel streamlines agrees with Darcy′s fi ltration law for an anisotropic medium. The equations of motion and continuity reduced to an equation of telegraphy enabled us to construct relations for the wave number, the absorption and attenuation coefficients, and the velocity of filtration waves. The expression for the phase velocity, the absorption coefficient, and the wave number of filtration waves has made it possible to investigate the correlation between this velocity and the velocity of elastic acoustic waves and the dependence on frequency. The extended theory of fi ltration-wave pressure fields refines the ideas of propagation of monochromatic filtration wave disturbances in a porous medium and confirms the substantial decrease in the velocity in the low-frequency region compared to the velocity of propagation of elastic waves.

The contact problem for a double-layer cylindrical base with account of friction forces

The contact problem of a double-layer cylindrical base is discussed with account of friction forces. The problem is reduced to an integral equation of the first kind in relation to unknown contact stresses. A direct method of collocation is used to solve it, enabling us to obtain sufficiently accurate solutions for virtually any values of the parameters. The contact stresses and the contact-zone area are calculated for various material and geometrical parameters of the base layers.

The stress-deformed state of a packet of cylindrical shells taking account of friction

We propose a method of determining the contact pressures between the shells in a packet under the influence of nonlinear internal and constant external pressure. Using the equations of the general moment theory of shells we determine the stress-deformed state of a packet of finite cylindrical shells taking account of frictional forces on the contacting surfaces. One table. Bibliography: 10 titles.

Variational principles and mathematical methods of solving boundary-value problems for piecewise uniform nonlinear media

We give a variational formulation and a scheme for numerical solution of boundary-value problems for piecewise-uniform nonlinear media taking account of frictional forces. We solve the problem of determining the stressed state of a thick three-layer cylinder of elastoplastic material with linear reinforcing under the action of internal pressure and an axially symmetric temperature field.

Contact problem for a preliminarily stressed halfplane in the case of a system of rigid dies, taking account of frictional forces

Contact problem for a preliminarily stressed halfplane in the case of a system of rigid dies, taking account of frictional forces

Cylindrical flexure of two-layer plate taking account of frictional forces

Cylindrical flexure of two-layer plate taking account of frictional forces

Aerodynamic coefficients of non-conical bodies with a star-shaped transverse cross section

It is well known that, in a supersonic flow, the wave resistance of a body of non-round transverse cross section can be less than the resistance of an equivalent body of revolution with the same length and volume. Starting from 1959, when an exact solution was obtained to the problem of supersonic flow around conical bodies with a pyramidal system of flat discontinuities [1], a number of publications have appeared [2–5] developing this direction. Article [3] pointed out the possibility of achieving a flow with reflected shock waves, normal to the faces of a pyramidal body, by selection of the form of the leading edge. In [6, 7], using the Newton resistance law, bodies were constructed with a transverse cross section of a star-shaped form, having a wave resistance several times less than for an equivalent body of revolution. Just such forms, with certain limitations, have the least wave resistance and retain optimality with respect to the total resistance, taking approximate account of friction forces. Still two more exact solutions were then found, corresponding to flow around star-shaped bodies with regular and Mach interaction between shock waves [8, 9]. At a seminar of the Institute of Mechanics of Moscow State University, G. G. Chernyi advanced the postulation of the existence of certain classes of three-dimensional bodies not having the property of similitude and retaining optimality with respect to determined characteristics, for example, the resistance, the aerodynamic quality, or the torque, and stated partial problems of finding various forms of optimal bodies. Classes of bodies, optimal with respect to the resistance, were obtained within the framework of the Newton theory; the bodies consisted of helical surfaces, as well as of sections of planes and conical surfaces, formed by straight lines connecting the leading edges with a round contour. As a result of calculations using the Newton theory and experimental investigations it was established that bodies with a wedge-shaped nose part, with determined geometric parameters, have greater values of the lifting and of the aerodynamic quality than round cones [10]. The possibility of lowering the resistance and increasing the aerodynamic quality of aircraft by giving them shapes of the transverse cross section in the form of a star [11–14] leads to new investigations of three-dimensional bodies which retain optimality with respect to their aerodynamic characteristics, and are used in conjunction with bodies of revolution. This latter factor is of decisive importance with the use of such configurations as the nose part of the aircraft, or of a multi-step diffusor. The present article gives the results of an experimental investigation of flow around two classes of such bodies: multi-wedge and helical.

Taking account of frictional forces in the contact region between a circular punch and an elastic half-space

Taking account of frictional forces in the contact region between a circular punch and an elastic half-space

A cylindrical shell with an elastic filler taking account of friction forces

A cylindrical shell with an elastic filler taking account of friction forces